# Convergence of a first-order consensus-based global optimization algorithm

arXiv: https://arxiv.org/abs/1910.08239 · HTML: https://mlsanity.com/paper/1910.08239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization](https://mlsanity.com/paper/2511.21466/) (2025)

## Abstract (arXiv)

Global optimization of a non-convex objective function often appears in large-scale machine-learning and artificial intelligence applications. Recently, consensus-based optimization (in short CBO) methods have been introduced as one of the gradient-free optimization methods. In this paper, we provide a convergence analysis for the first-order CBO method in citeC-J-L-Z. Prior to the current work, the convergence study was carried out for CBO methods on corresponding mean-field limit, a Fokker-Planck equation, which does not imply the convergence of the CBO method it per se. Based on the consensus estimate directly on the first-order CBO model, we provide a convergence analysis of the first-order CBO method citeC-J-L-Z without resorting to the corresponding mean-field model. Our convergence analysis consists of two steps. In the first step, we show that the CBO model exhibits a global consensus time asymptotically for any initial data, and in the second step, we provide a sufficient condition on system parameters--which is dimension independent-- and initial data which guarantee that the converged consensus state lies in a small neighborhood of the global minimum almost surely.